Which ever route you go down, It's not gonna be cheap! Hardwood is around £7 a board foot, only available up to 9'' wide, so would need jointing. How good are you at woodwork? That's one of the reasons chests are so expensive! What size are you looking for?

Most timber merchants sell timber priced by the cubic foot rather than the American board foot.They tend not to sell boards in cut to size pieces, you have to buy the entire board.Prices tend to vary by thickness and width of boards, ramping up quite quickly.For Ash expect to pay £30 upwards a cubic foot, Oak around £50 upwards a cubic foot.The last one inch Oak boards I bought were 13 inch wide and nine to ten foot long, cost about £110 for two, but I straight to the sawmill for them.Of course then you have to have the woodworking tools and skills to turn the timber into something useful.

Whichever route you decide to go down, you first need to decide on a particular type of chest and how much decoration it will have.

"Medieval" is far too generic a term - is it 11th, 12th, 13th, 14th, 15th century? Will it have pin hinges (the earlier method) or metal strap-hinges (later)? Will it be of hutch construction or some other style? Will it be carved, painted or plain? Will it be of hardwood (very heavy but more authentic), or will you make it lighter for modern transport using softwood?

Period chests were not generally intended to be mobile - the strongbox type (either an actual trunk or an oak chest bound in iron) was deliberately made too heavy to lift and sometimes even secured to a wall with chains and staples. Domestic chests would have locks even if there was no other security measure, since they stored books, expensive clothing, money and valuables - coffer and chest keys survive from every stage in the medieval era.

Surviving chests are mainly Church items, again used for storing valuables and money, but they do provide a taste of how contemporary domestic chests would be made and decorated. Sadly out of print, "Church Chests of the Twelfth and Thirteenth Centuries in England" by P Mainwaring Johnston, The Caber Press 2001, is a very detailed source for chest and coffer construction and decoration methods, if you can source a copy (mine came from a bookshop in the USA).

If I were to plan a project like that I would settle on an authentic period style, draw it out and calculate all the measurements on paper and only then think about what and how much timber to buy.

As an example, his is the pin hinged church chest at Bosham, Sussex; it is thought to date to around 1210 and it is 5' 6" long, 1' 9" wide and 2' 2" tall: